My visitor clicks on 1 out of 10 different hyperlinks that al lead to the same form they have to fill out. On the top of the form I want to state: "you chose link1 (or 2 or 3...)". And after submitting the form, 'link1' should be inserted in my table, just like the fields the visitor manually entered.

No, the links refer to an sql table I created.
The links are in fact thumbnails. It should work like this:

"Elect our new class president, please click on a picture and fill out your election form"
So there are several pics of elegable class presidents. If you click on either of them, you end up in a form, which states the name of the person you chose. You fill in your name and click on submit. Now my sql table "votes" should receive both the name of the chosen class president and the name of the person who voted.

OK, I inserted the parameter like you said:
<a href="formpage.php?person=1"><img=blablabla></a>

I am sorry for being this ignorent about all this, but what do I do next?
Once I clicked on the img, I am in the form. If person1=John Doe ,how can I state: "you chose John Doe, now fill in your name and submit."

On the form page you'll recieve a variable which will be $_GET['person']. You can use your own script now to work out who the person is based on this variable, and you can also write a 'hidden' tag in your form so it'll submit it with the rest of the data!

The sql table I created has only one column, with the names of the eligable class presidents. For instance, John Doe is the 2nd person in the table.
On top of the (html-)form I want to state: "You chose John Doe."

I have already attached : <a href="formpage.php?person=1"><img=blablabla></a>
to each thumbnail. Now what to do??

on the form page you now know that the person wants to vote on person 1, in other words John Doe, use that to build you're form!
on that page you will have to pass that data to the next page, wich enters the data into the database.
You can use a hidden field for that.

On the last page (wich enters the data into the database) you will have to make you're query to enter the data.
for wich you will have to use the variables you passed from the form.

How that query looks depends entirely on what fields you got in you're table.

What you need is 2 databases:
One will hold the candidate information (id and name) and the other will hold information on the votors (name, vote, etc).

On the first page list all the candidates using the code you're using:
<a href="formpage.php?person=X"><img src="picture_john_doe.jpg"></a>
replacing X for the ID of that person.

When someone clicks on it, they'll get taken to a form page. Use the $_GET['person'] value to work out who they voted for ("select name from candidates where ID=".$_GET['person']) and you can use this to display "You have selected John Doe" or whatever. Also, include this in a hidden field in your form (<input type='hidden' name='vote' value='X'>) so when the user submits his details, the vote will be registered as well!

I think you've bitten off more than you can chew. I did suspect so, but didn't want to say. You need to learn how to access and manipulate a MySQL database with PHP, and also how to control variables and use them in presentation of data before you can think about inserting and retrieving form data!